# Re: effect of magnitude and direction on the organpipe's note

I am reading "Relativity: The Special and General Theory" by Albert Einstein, and in orden to continue reading with full understanding, I would like someone to please clarify one thing for me (or most likely more than one).

In the section dealing with "The Principle of Relativity (in the restricted sense), Einstein explains that "In the general laws of nature... ...with reference to K, the magnitude and direction of the velocity of the carriage would necessarily play a part." He goes on to exemplify saying that "the note emitted by an organpipe placed with its axis parallel to the direction of travel would be different from that emitted if the axis of the pipe were placed perpendicular to this direction."

I would like to know if I am understanding this right. Is the fact that the organ's note will sound different, depending on the position of its axis, due to the doppler effect? Is this difference what he calls in the following paragraph the anisotropic property resulting from the difference of the position of the axis of the organpipe? If this was the case, then I understand that if the axis of the organ is parallel to the direction of travel of the carriage, then the organ would be moving along with the carriage and the note would sound normal to a listerer on the carriage but different to someone on the enbankment. Conversely, if the axis of the organ is perpendicular to the direction of the carriage then the note would sound normal to a listener in the enbankment but different to someone traveling in the carriage.

Am I in the right trend of thought? Or did I go off the course?

I would appreciate your comments.

## Answers and Replies

Not an expert, but this is how it looks to me...

Your quote is leaving out the important part... he is describing what would be expected of Galilean co-ordinate systems if the principle of relativity (in the restricted sense) did not hold. The difference in pitch from different orientations is an example of what might happen, but has nothing to do with Doppler.

He might have used a better example than pitch because so many will jump to the Doppler effect, but that effect is irrelevant to what he meant to express. The note is being emitted in the carriage and the pitch of the emitted note is "there"... he is positing that the pitch might change "there" at the emission point based on orientation if the relativity principle did not hold; nothing to do with how it might be heard from a distance subject to motion of the carriage.

So, it is not a fact that the organ note would sound different... he is suggesting that if it were a fact that the principle of relativity did not hold, then something like this might be observed. It is an unfortunate example.

Doppler is when you hear a pitch shift due to relative motion with respect to the source. The shift is about one semi-tone for each increment of 10 mph.

His example might also be a little confusing because relativity covers uniform relative motion, orientations of rotation, and arbitrary position locations.. The different organ pipe directions are particular rotation orientations, but his example has them also translating in uniform motions... he maybe should have used a simple example ... maybe temperature or pressure or something... like the temperature to boiling water at STP or the rate at which a pressure difference moves a piston.